## Applied Regression Analysis and Experimental DesignFor a solid foundation of important statistical methods, this concise, single-source text unites linear regression with analysis of experiments and provides students with the practical understanding needed to apply theory in real data analysis problems. Stressing principles while keeping computational and theoretical details at a manageable level, Applied Regression Analysis and Experimental Design features an emphasis on vector geometry of least squares to unify and provide an intuitive basis for most topics covered ... abundant examples and exercises using real-life data sets clearly illustrating practical problems of data analysis ... essential exposure to Minitab and Genstat computer packages, including computer printouts ... and important background material such as vector and matrix properties and the distributional properties of quadratic forms. Designed to make theory work for students, this clearly written, easy-to-understand work serves as the ideal text for courses in Regression, Experimental Design, and Linear Models in a broad range of disciplines. Moreover, applied statisticians, biometricians, and research workers in applied statistics will find the book a useful reference for the general application of the linear model. Book jacket. |

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### Contents

Fitting a Model to Data | 1 |

Goodness of Fit of the Model | 30 |

Which Variables Should Be Included in the Model | 56 |

4 Peculiarities of Observations | 84 |

The Experimental Design Model | 106 |

Assessing the Treatment Means | 126 |

Blocking | 153 |

Extensions to the Model | 182 |

Appendix A Review of Vectors and Matrices | 212 |

Appendix B Expectation Linear and Quadratic Forms | 219 |

References | 229 |

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### Common terms and phrases

adjusted ANALYSIS OF VARIANCE ANOVA table Appendix assumptions Boron calculated Chapter columns Computer Focus Computer Pairing confidence intervals confounded constant contrast correlation covariate degrees of freedom dependent variable deviations estimated coefficients example experimental design experimental units F-statistic F-test Figure Focus Fd Tl full model GENSTAT give hypothesis included incomplete block independent least squares linear model main effects main plot mean square measure method normal equations number of observations orthogonal Pairing Fd Tl Pairing Tl Fd parameters Phos polio possible predicted values predictor variables problem projection matrix quadratic R-SQUARED random randomly reduced model REGRESSION ANALYSIS replication sample Section significant sodium SOURCE OF VARIATION split plot squares for regression standard error Statistical STRATUM studentized residuals sum of squares term TOTAL transformation treatment difference treatment effect treatment means treatment sum Trtmnt VARIATION DF SS weighted least squares yield zero